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Thursday, January 5, 2017 2:14

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In FB I was made a question about general aspects of TGD. It was impossible to answer the question with few lines and I decided to write a blog posting. I am sorry for typos in the hastily written text. A more detailed article Can one apply Occam’s razor as a general purpose debunking argument to TGD? tries to emphasize the simplicity of the basic principles of TGD and of the resulting theory.

**A. In what aspects TGD extends other theory/theories of physics? **

I will replace “extends” with “modifies” since TGD also simplifies in many respects. I shall restrict the considerations to the ontological level which to my view is the really important level.

- Space-time level is where TGD started from. Space-time as an abstract 4-geometry is replaced as space-time as 4-surface in M
^{4}× CP_{2}. In GRT space-time is small deformation of Minkowski space.

In TGD both Relativity Principle (RP) of Special Relativity (SRT) and General Coordinate Invariance (GCI) and Equivalence Principle (EP) of General Relativity hold true. In GRT RP is given up and leads to the loss of conservation laws since Noether theorem cannot be applied anymore: this is what led to the idea about space-time as surface in H. Strong form of holography (SH) is a further principle reducing to strong form of GCI (SGCI).

One important aspect is a new view about time: experienced time and geometric time are not one and same thing anymore although closely related. ZEO explains how the experienced flow and its direction emerges. The prediction is that both arrows of time are possible and that this plays central role in living matter.

ZEO implies that conservation laws formulated only in the scale of given CD do not anymore fix select just single solution of field equations as in classical theory. Theories are strictly speaking impossible to test in the old classical ontology. In ZEO testing is possible be sequence of state function reductions giving information about zero energy states.

In principle transition between any two zero energy states – analogous to events specified by the initial and final states of event – is in principle possible but Negentropy Maximization Principle (NMP) as basic variational principle of state function reduction and of consciousness restricts the possibilities by forcing generation of negentropy: the notion of negentropy requires p-adic physics.

Zero energy states are quantum superpositions of classical time evolutions for 3-surfaces and classical physics becomes exact part of quantum physics: in QFTs this is only the outcome of stationary phase approximation. Path integral is replaced with well-defined functional integral- not over all possible space-time surface but pairs of 3-surfaces at the ends of space-time at opposite boundaries of CD.

ZEO leads to a theory of consciousness as quantum measurement theory in which observer ceases to be outsider to the physical world. One also gets rid of the basic problem caused by the conflict of the non-determinism of state function reduction with the determinism of the unitary evolution. This is obviously an extension of ordinary physics.

The most important applications are to biology, where quantum coherence could be understood in terms of a large value of h_{eff}/h. The large n phases resembles the large N limit of gauge theories with gauge couplings behaving as α ∝ 1/N used as a kind of mathematical trick. Also gravitation is involved: h_{eff} is associated with the flux tubes mediating various interactions (being analogs to wormholes in ER-EPR correspondence). In particular, one can speak about h_{gr}, which Nottale introduced originally and h_{eff}= h_{gr} plays key role in quantum biology according to TGD.

** B. In what sense TGD is simplification/extension of existing theory?**

- Classical level: Space-time as 4-surface of H means a huge reduction in degrees of freedom. There are only 4 field like variables – suitably chosen 4 coordinates of H=M
^{4}× CP_{2}. All classical gauge fields and gravitational field are fixed by the surface dynamics. There are no primary gauge fields or gravitational fields nor any other fields in TGD Universe and they appear only at the QFT limit.

GRT limit would mean that many-sheeted space-time is replaced by single slightly curved region of M^{4}. The test particle – small particle like 3-surface – touching the sheets simultaneously experience sum of gravitational forces and gauge forces. It is natural to assume that this superposition corresponds at QFT limit to the sum for the deviations of induced metrics of space-time sheets from flat metric and sum of induce gauge potentials. These would define the fields in standard model + GRT. At fundamental level effects rather than fields would superpose. This is absolutely essential for the possibility of reducing huge number field like degrees of freedom. One can obviously speak of emergence of various fields.

A further simplication is that only preferred extremals for which data coding for them are reduced by SH to 2-D string like world sheets and partonic 2-surace are allowed. TGD is almost like string model but space-time surfaces are necessary for understanding the fact that experiments must be analyzed using classical 4-D physics. Things are extremely simple at the level of single space-time sheet.

Complexity emerges from many-sheetedness. From these simple basic building bricks – minimal surface extremals of Kähler action (not the extremal property with respect to Kähler action and volume term strongly suggested by the number theoretical vision plus analogs of Super Virasoro conditions in initial data) – one can engineer space-time surfaces with arbitrarily complex topology – in all length scales. An extension of existing space-time concept emerges. Extremely simple locally, extremely complex globally with topological information added to the Maxwellian notion of fields (topological field quantization allowing to talk about field identify of system/field body/magnetic body.

Another new element is the possibility of space-time regions with Euclidian signature of the induced metric. These regions correspond to 4-D “lines” of general scattering diagrams. Scattering diagrams has interpretation in terms of space-time geometry and topology.

The key principle is geometrization of the entire quantum theory, not only of classical fields geometrized by space-time as surface vision. This requires geometrization of hermitian conjugation and representation of imaginary unit geometrically. Kähler geometry for WCW makes this possible and is fixed once Kähler function defining Kähler metric is known. Kähler action for a preferred extremal of Kähler action defining space-time surface as an analog of Bohr orbit was the first guess but twistor lift forced to add volume term having interpretation in terms of cosmological constant.

Already the geometrization of loop spaces demonstrated that the geometry – if it exists – must have maximal symmetries (isometries). There are excellent reasons to expect that this is true also in D=3. Physics would be unique from its mathematical existence!

** C. What is the hypothetical applicability of the extension – in energies, sizes, masses etc? **

TGD is a unified theory and is meant to apply in all scales. Usually the unifications rely on reductionistic philosophy and try to reduce physics to Planck scale. Also super string models tried this and failed: what happens at long length scales was completely unpredictable (landscape catastrophe).

Many-sheeted space-time however forces to adopt fractal view. Universe would be analogous to Mandelbrot fractal down to CP_{2} scale. This predicts scaled variants of say hadron physics and electroweak physics. p-Adic length scale hypothesis and hierarchy of phases of matter with h_{eff}=n×h interpreted as dark matter gives a quantitative realization of this view.

- p-Adic physics shows itself also at the level of real physics. One ends up to the vision that particle mass squared has thermal origin: the p-adic variant of particle mass square is given as thermal mass squared given by p-adic thermodynamics mappable to real mass squared by what I call canonical identification. p-Adic length scale hypothesis states that preferred p-adic primes characterizing elementary particles correspond to primes near to power of 2: p=about 2
^{k}. p-Adic length scale is proportional to p_{1/2}.

This hypothesis is testable and it turns out that one can predict particle mass rather accurately. This is highly non-trivial since the sensivity to the integer k is exponential. So called Mersenne primes turn out to be especially favoured. This part of theory was originally inspired by the regularities of particle mass spectrum. I have developed arguments for why the crucial p-adic length scale hypothesis – actually its generalization – should hold true. A possible interpretation is that particles provide cognitive representations of themselves by p-adic thermodynamics.

** D. What is the leading correction/contribution to physical effects due to TGD onto particles, interactions, gravitation, cosmology?**

- Concerning particles I already mentioned the key predictions.
- The existence of scaled variants of various particles and entire branches of physics. The fundamental quantum numbers are just standard model quantum numbers code by CP
_{2}geometry.

- The existence of scaled variants of various particles and entire branches of physics. The fundamental quantum numbers are just standard model quantum numbers code by CP

The failure of QFTs to describe bound states of say hydrogen atom could be second example: many-sheetedness and identification of bound states as single connected surface formed by proton and electron would be essential and taken into account in wave mechanical description but not in QFT description.

Minimal surfaces carrying no K&aum;lher field would be the basic model for gravitating system. Minimal surface equation are non-linear generalization of d'Alembert equation with gravitational self-coupling to induce gravitational metric. In static case one has analog for the Laplace equation of Newtonian gravity. One obtains analog of gravitational radition as “massless extremals” and also the analog of spherically symmetric stationary metric.

Blackholes would be modified. Besides Schwartschild horizon which would differ from its GRT version there would be horizon where signature changes. This would give rise to a layer structure at the surface of blackhole.

One can look at the situation also at the fundamental level. The addition of volume term implies that the only RW cosmology realizable as minimal surface is future light-cone of M^{4}. Empty cosmology which predicts non-trivial slightly too small redshift just due to the fact that linear Minkowski time is replaced with lightcone proper time constant for the hyperboloids of M^{4}_{+}. Locally these space-time surfaces are however deformed by the addition of topologically condensed 3-surfaces representing matter. This gives rise to additional gravitational redshift and the net cosmological redshift. This also explains why astrophysical objects do not participate in cosmic expansion but only comove. They would have finite size and almost Minkowski metric.

The gravitational redshift would be basically a kinematical effect. The energy and momentum of photons arriving from source would be conserved but the tangent space of observer would be Lorentz-boosted with respect to source and this would course redshift.

The very early cosmology could be seen as gas of arbitrarily long cosmic strings in H (or M^{4}) with 2-D M^{4} projection. Horizon would be infinite and TGD suggests strongly that large values of h_{eff} makes possible long range quantum correlations. The phase transition leading to generation of space-time sheets with 4-D M^{4} projection would generate many-sheeted space-time giving rise to GRT space-time at QFT limit. This phase transition would be the counterpart of the inflationary period and radiation would be generated in the decay of cosmic string energy to particles.

For a summary of earlier postings see Latest progress in TGD.